Permutations and Combinnations

Probability Level 2

A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?

168 41 36 26

Ram Biradar by Ram Biradar , 24, India

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1 solution

Ram Biradar
Oct 18, 2018

Let us make the following cases: Case (i) Boy borrows Mathematics Part II, then he borrows Mathematics Part I also. So the number of possible choices, 8 - 2 = 6 out of which 1 is to be chosen as 2 are must. 6C1 = 6. Case (ii) Boy does not borrow Mathematics Part II, then the number of possible choices is 7C3 = 35. Hence, the total number of possible choices is 35 + 6 = 41.

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Sorry, but I am confused about your solution. If the boy does not borrow Mathematics Part II then he does not borrow Part I either, so doesn't he have to choose his 3 books from the remaining 6, or 6 C 3 ^6C_3 , which is 20? This would give a total of 26. Please explain.

Richard Costen - 2 years, 7 months ago

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If he borrows part II then he must borrow the part I book. but it's not specified that if he borrows the part-I he has to borrow part II(may or may not borrow). So the number of remaining choices would be 7.

Ram Biradar - 2 years, 7 months ago

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I missed that. Thanks

Richard Costen - 2 years, 7 months ago

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